R/annuity.arith.R

In FinancialMath: Financial Mathematics for Actuaries

annuity.arith=function(pv=NA,fv=NA,n=NA,p=NA,q=NA,i=NA,ic=1,pf=1,imm=TRUE,plot=FALSE){

  all=list(pv,fv,n,p,q,i,ic,pf,imm,plot)
  #NULL
  if(any(lapply(all,is.null)==T)) stop("Cannot input any variables as NULL.")
  #Length
  if(any(lapply(all,length) != 1)==T) stop("All inputs must be of length 1.")
  #Numeric
  num2=list(pv,fv,n,p,i,ic,pf,q)
  na.num2=num2[which(lapply(num2,is.na)==F)]
  if(any(lapply(na.num2,is.numeric)==F)) stop("pv, fv, n, p, q, i, ic, and pf must be numeric.")
  #NA
  nalist=list(ic,pf,imm,plot)
  if(any(lapply(nalist,is.na)==T)) stop("Cannot input ic, pf, imm, and plot as NA.")
  #Logical
  stopifnot(is.logical(imm),is.logical(plot))

  num=c(pv,fv,n,p,i,ic,pf)
  NA.Neg=array(num)
  NA.Neg.Str=c("pv","fv","n","p","i","ic","pf")
  app=apply(NA.Neg,1,is.na)
  #Positive
  na.s=which(app==F & NA.Neg<=0)
  if(length(na.s)>0) {errs=paste(NA.Neg.Str[na.s],collapse=" & ")
  stop(cat("Error: '",errs, "' must be positive real number(s).\n"))}
  #Infinite
  na.s2=which(app==F & NA.Neg==Inf)
  if(length(na.s2)>0) {errs=paste(NA.Neg.Str[na.s2],collapse=" & ")
  stop(cat("Error: '",errs, "' cannot be infinite.\n"))}

  test=c(n,i);t1=length(test[which(is.na(test))])
  test2=c(pv,fv);t2=length(test2[which(is.na(test2))])
  test3=c(p,q);t3=length(test3[which(is.na(test3))])
  test4=c(n,i,p,q);t4=length(test4[which(is.na(test4))])
  if(t2 == 0) stop("Cannot specify both pv and fv.")
  if(t1 >= 2) stop("Too many unknowns.")
  if(t3 >= 2) stop("Cannot have both p and q unknown")
  if(t4==0 & t2==0) stop("No unknowns specified.")
  if(t4==1 & t2==2) stop("Too many unknowns.")
  if(t1==0 & t3==0 & t2==1) stop("one of n, p, q, or i must be unknown if either pv or fv is known.")

  if(!is.na(n) & n !=round(n)) stop("n must be a positive integer")
  if(!is.na(p) & !is.na(q) & p+q<=0) stop("q is too small.")
  if(is.na(n)) sn=T else sn=F
  if(!is.na(p) & !is.na(q) & !is.na(n) & p+q*(n-1)<0) stop("Payments become negative.")

  nom1=NA;nom2=NA

  if(is.na(i)){
    if(imm==T) {
      if(is.na(pv)) {i=round(Re(polyroot(c(-fv+p+q*(n-1),rev(seq(from=p,by=q,length.out=n-1)))))-1,8)
      i=i[which(round((p*(1-(1+i)^-n)/i+q*((1-(1+i)^-n)/i-n*(1+i)^-n)/i)*(1+i)^n,0)==round(fv,0))]}
      if(is.na(fv)) {i=round(1/Re(polyroot(c(-pv,(seq(from=p,by=q,length.out=n)))))-1,8)
      i=i[which(round((p*(1-(1+i)^-n)/i+q*((1-(1+i)^-n)/i-n*(1+i)^-n)/i),2)==round(pv,2))]}
    }
    if(imm==F) {
      if(is.na(pv)) {i=round(Re(polyroot(c(-fv,rev(seq(from=p,by=q,length.out=n)))))-1,8)
      i=i[which(round((p*(1-(1+i)^-n)/i+q*((1-(1+i)^-n)/i-n*(1+i)^-n)/i)*(1+i)^(n+1),0)==round(fv,0))]}
      if(is.na(fv)) {i=round(1/Re(polyroot(c(-pv+p,(seq(from=p+q,by=q,length.out=n-1)))))-1,8)
      i=i[which(round((p*(1-(1+i)^-n)/i+q*((1-(1+i)^-n)/i-n*(1+i)^-n)/i)*(1+i),0)==round(pv,0))]}
    }
    if(length(i)>1) {if(any(i>0)) i=i[which(i>0)] else i=i[1];i=i[1]}
    eff.i=(1+i)^pf-1
    n.i=(1+eff.i)^(1/ic)-1
    if(ic != 1) nom1=n.i*ic
    if(pf != 1 & pf != ic) nom2=i*pf
    i=n.i*ic
  }

  eff.i=(1+i/ic)^(ic)-1
  int=(1+eff.i)^(1/pf)-1
  if(imm==T) r=1 else r=1+int
  if(ic !=1) nom1=((1+eff.i)^(1/ic)-1)*ic
  if(pf != ic & pf !=1) nom2=((1+eff.i)^(1/pf)-1)*pf

  if(is.na(p)){
    if(is.na(fv)) p=(pv/r-q*((1-(1+int)^-n)/int-n*(1+int)^-n)/int)/((1-(1+int)^-n)/int)
    if(is.na(pv)) p=(fv/r/(1+int)^n-q*((1-(1+int)^-n)/int-n*(1+int)^-n)/int)/((1-(1+int)^-n)/int)
  }

  if(is.na(q)){
    if(is.na(fv)) q=(pv/r-p*(1-(1+int)^-n)/int)/(((1-(1+int)^-n)/int-n*(1+int)^-n)/int)
    if(is.na(pv)) q=(fv/r/(1+int)^n-p*(1-(1+int)^-n)/int)/(((1-(1+int)^-n)/int-n*(1+int)^-n)/int)
  }

  if(is.na(n)){
    if(is.na(pv)) h=fv else h=pv
    for(g in 0:1000){
      if(is.na(fv)) h=h-r*(p+q*g)/(1+int)^g else h=h-(p+q*g)
      if(h<=0) {g=g+1;break}
    }
    n=seq(from=g/4,to=3*g,by=.0001)
    if(is.na(fv)) n=n[which(round(r*(p*(1-(1+int)^-n)/int+q*((1-(1+int)^-n)/int-n*(1+int)^-n)/int),0)==round(pv,0))]
    if(is.na(pv)) n=n[which(round(r*(p*(1-(1+int)^-n)/int+q*((1-(1+int)^-n)/int-n*(1+int)^-n)/int)*(1+int)^n,1)==round(fv,1))]
    n=median(n)
  }

  if(is.na(pv)) {
    pv=(p*(1-(1+int)^-n)/int+q*((1-(1+int)^-n)/int-n*(1+int)^-n)/int)*r}
  if(is.na(fv)) {
    fv=(p*(1-(1+int)^-n)/int+q*((1-(1+int)^-n)/int-n*(1+int)^-n)/int)*r*(1+int)^n}

  if(plot==T){
    if(sn==F){
      plot.new()
      plot(0,0,type="n",axes=F,ann=F,xlim = c(0,ceiling(n)+1),ylim=c(0, 10))
      axis(1,at=seq(0,ceiling(n)),labels=seq(0,ceiling(n)),line=-8)
      if(imm==T){
        text(seq(1,ceiling(n)),rep(5.5,ceiling(n)),labels=seq(round(p,2),by=round(q,2),length.out=ceiling(n)),cex=.75)
      }
      if(imm==F){
        text(seq(0,ceiling(n)-1),rep(5.5,ceiling(n)),labels=seq(round(p,2),by=round(q,2),length.out=ceiling(n)),cex=.75)
      }
      if(pf != 1) axis(1,at=seq(0,ceiling(n),by=pf),labels=seq(0,ceiling(n),by=pf)/pf,line=-5,col="blue")
      text(.05*n,7.2,labels=round(pv,2),cex=.85)
      text(.05*n,7.7,labels="PV")
      text(n-.05*n,7.2,labels=round(fv,2),cex=.85)
      text(n-.05*n,7.7,labels="FV")
      text(n/2,10,labels="Time Diagram",cex=1.2)
      text(n/2,9.4,labels=if(q != 0) "Arithmetic Annuity" else "Level Annuity",cex=1)
      text(n*.4,8.5,bquote("Eff Rate "== .(round(eff.i,4))),cex=.85)
      if(pf != 1) text(n*.4,7.8,bquote( i^(.(pf))== .(round(int*pf,4))),cex=.85)
      i.ic=((1+eff.i)^(1/ic)-1)*ic
      if(ic != 1 & ic != pf) text(n*.4,7.1,bquote( i^(.(ic))== .(round(i.ic,4))),cex=.85)
      if(pf==1) legend(0,1,legend="Years",lty=1,bty="n") else legend(0,1,legend=c("Periods","Years"),lty=1,col=c("black","blue"),bty="n",ncol=2)
    } else warning("No time diagram is provided when solving for n.\n") }

  if(pf==1) {years=n;n=NA} else years=n/pf
  out=c(pv,fv,p,q,eff.i,nom1,nom2,n,years)
  m.out=matrix(out,nrow=length(out))
  rownames(m.out)=c("PV","FV","P","Q","Eff Rate",paste("i^(",round(ic,2),")",sep=""),
                    paste("i^(",round(pf,2),")",sep=""),"Periods","Years")
  na=apply(m.out, 1, function(x) all(is.na(x)))
  m.out=as.matrix(m.out[!na,])
  if(round(q,2)==0) m="Level Annuity" else m="Arithmetic Annuity"
  colnames(m.out)=m
  return(m.out)
}